This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A266508 #36 Feb 16 2025 08:33:28
%S A266508 1,11,101,1011,10101,101011,1010101,10101011,101010101,1010101011,
%T A266508 10101010101,101010101011,1010101010101,10101010101011,
%U A266508 101010101010101,1010101010101011,10101010101010101,101010101010101011,1010101010101010101,10101010101010101011
%N A266508 Binary representation of the n-th iteration of the "Rule 28" elementary cellular automaton starting with a single ON (black) cell.
%C A266508 Rule 156 also generates this sequence.
%C A266508 Also, the binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 678", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283641.
%H A266508 Robert Price, <a href="/A266508/b266508.txt">Table of n, a(n) for n = 0..1000</a>
%H A266508 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266508 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A266508 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266508 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266508 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-10).
%F A266508 From _Colin Barker_, Dec 30 2015 and Apr 16 2019: (Start)
%F A266508 a(n) = (44 - 45*(-1)^n + 10^(2+n))/99.
%F A266508 a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n>2.
%F A266508 G.f.: (1+x-10*x^2) / ((1-x)*(1+x)*(1-10*x)).
%F A266508 (End)
%F A266508 a(n) = floor((100*10^n + 89)/99). - _Karl V. Keller, Jr._, Sep 04 2021
%t A266508 rule=28; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]],{k,1,rows}] (* Binary Representation of Rows *)
%o A266508 (Python) print([(100*10**n + 89)//99 for n in range(50)]) # _Karl V. Keller, Jr._, Sep 04 2021
%Y A266508 Cf. A266502, A283641, A283642.
%K A266508 nonn,easy
%O A266508 0,2
%A A266508 _Robert Price_, Dec 30 2015